An Israeli lawmaker has been invited to Syria to discuss a recent Syrian offer to renew peace talks between the sworn enemies, Israel Radio has said.
Events in the region have put pressure on Assad
The MP, from PM Ariel Sharon's Likud Party, could go to Egypt to discuss the offer with officials there, it said.
Syria has recently made overtures to both Israel and the US, which is threatening Syria with sanctions.
In another development, an Israeli army helicopter fired two missiles at a car in Gaza, injuring several people.
Correspondents say the attack happened in the Rimal area in which the Palestinian militant group Hamas operates.
Israel Radio did not say whether the lawmaker, who was not identified, would meet Syrian officials in Egypt or if he would travel to Damascus.
US SANCTIONS PACKAGE
End support for "terrorists"
Pull troops out of Lebanon
End acquisition and production of weapons of mass destruction and long-range ballistic missiles
Prevent terrorists and weapons from entering Iraq
Ban on sales of dual-use technology
Prohibition of operations by US businesses
Limits on Syrian airline flights within US
Reduction of diplomatic contacts
Freeze on Syrian assets in US
However, it reported that sources in Mr Sharon's office said the lawmaker would not be a government representative.
It also said that Mr Sharon had told his cabinet that any peace talks with Syria should re-start from scratch.
Damascus has been calling for the resumption of the talks from where the two sides left off in 2000.
The two sides almost clinched a deal there that included an Israeli offer to return most of the Golan Heights, captured in 1967, in exchange for security guarantees from Syria.
The Syrian offer came soon after Washington approved a law threatening punishment if Damascus does not rein in militants and stop seeking weapons of mass destruction.
Experts say Syrian President Bashar al-Assad is keen to show he is ready to engage in constructive talks in light of recent moves by Libya and Iran to open their weapons programmes to international inspections.
The Israeli Haaretz daily has urged Mr Sharon to use the chance and seriously consider the offer from Damascus.
"Even if Assad's motivation derives from strategic weakness rather than a sudden interest in Israel, his proposal still deserves serious and sincere scrutiny," the newspaper said in its editorial on Wednesday.
Syria and Israel fought three major conflicts - in 1948, 1967 and 1973.
Despite a recent Israeli air raid inside Syria, the border between the two countries remains relatively quiet.